The bank’s chairman, who on Wednesday presided over the premature resignation of Stephen Hester, has asked Anna Mann to find a successor to run the state-backed bank.

Her involvement suggests that neither Sir Philip nor Chancellor George Osborne had identified a successor to Mr Hester in advance, adding to speculation that his surprise departure was sparked by a sudden disagreement.

Ms Mann, of MWM Consulting, is one of the City’s most influential and best connected recruiters, having helped place Ian Davis as chairman of Rolls-Royce and Sir David Walker as chairman of Barclays.

Sir Philip has given her a list of the qualities that the ideal candidate would have to replace Mr Hester, who is due to leave the bank by the end of December. These include:

Þability to manage the business in a steady state, with the emphasis on management rather than restructuring;

Þability to develop and maintain strong and constructive relationships with all stakeholders;

Þability and willingness to endure in the job and deliver the privatisation strategy.

The most important quality is what Sir Philip is understood to have privately called “stakeholder management”, particularly regulators and investors, not least UK Financial Investments, which manages the Government’s 81pc stake in the bank.

Sir Philip is said to be “optimistic” that the challenge offered by the role should lead to a flurry of suitable candidates stepping forward.

The instructions specify that the search should be international, with a particular emphasis on the US, Canada and Australia. Nor has Sir Philip ruled out a non-banker for the job.

“It would be difficult to appoint a non-banker given the regulatory bar imposed since the credit crisis,” said one source, “but not impossible given the right candidate.”

Internal candidates are said to be in the frame but finance director Bruce van Saun is thought highly unlikely to throw his hat into the ring.

RBS sources suggested he was committed to returning to the US in October to lead the partial stock market float of the bank’s Citizens business.

News of Ms Mann’s appointment came after an eventful day which saw the bank’s shares slide by as much as 7pc at one stage, to close down 3.3pc at 315p, the biggest faller on the FTSE 100.

The slide came despite bullish comments from Sajid Javid, economic secretary to the Treasury. He said that the size and complexity of RBS has been “significantly reduced” since the financial crisis, and that the Government has always been clear it wants RBS “to become a more focused retail and commercial bank.”

He also accused the last Labour government of over-paying for RBS to the tune of £12bn.